1. Field of the Invention
The present invention relates to a color reproduction method, or more in particular to a color reproduction method to reproduce predetermined colors in multi-color printing, multi-color display, or the like.
2. Description of the Related Art
Colors of object surfaces, original documents and the like can be expressed in chromaticity expressed by tristimulus values (X,Y,Z) of CIE standard XYZ calorimetric system as generally known and can be normally specified on the chromaticity coordinates. It is also known that these tristimulus values X, Y, Z can be obtained if spectral distribution of reflected light from an object or transmitted light can be measured.
Recently, a necessity of color reproduction technology capable of faithfully reproducing colors desired by designers, for example, to evaluate design works in car design world has been stated. That is, in conducting design works by using computers, any chromaticity desired by designers, colors obtained by measurement or the like, images containing those colors and the like must be displayed on CRT display (hereinafter referred to as CRT) or reproduced faithfully by means of hard copy apparatus.
Additionally, information expressing images and colors can be transmitted between local remote places due to progress in recent information transmission network. In this case, the same information (colors and images) must be output with the same colors by means of CRTs and hard copiers on both sides.
FIG. 1 shows a general method for expressing any colors on CRT by additive mixture. According to this method, chromaticity 10 expressed by arbitrary tristimulus values (X,Y,Z) is converted to luminous intensities 14 of red, green and blue by means of a conversion processing 12 by a matrix using the chromaticities of respective fluorescent substances of red, green and blue (hereinafter referred to RGB) in the CRT and then converted to signal values 18 which are device values of the CRT. This conversion process 16 from the luminous intensity 14 to the signal value 18 is carried out according to a conversion method using a model formula indicating a relation between the luminous intensity and the signal value (for example, applied voltage) (see R. S. Bens, R. J. Motta and M. E. Gorzynski, CRT Colorimetry. Partv1: Theory and Practice, COLOR research and application Vol. 18 (No. 5), pp. 299-314, 1993) or according to a conversion method using a look-up table (hereinafter referred to as LUT) (see D. L. Post and C. S. Calhoun, An evaluation of methods for producing specific colors on CRTs, Proceedings of the Human Factors Society 31st Annual Meeting, pp. 1276-1280, 1987). By inputting this signal value 18 into the CRT display system (a system in which the CRT and D/A converter are combined which is referred to as CRT system), the color expressed by arbitrary tristimulus values (X,Y,Z) can be displayed.
To reproduce a color of arbitrary chromaticity on the CRT, it is necessary to know all the luminous intensities of fluorescent substances corresponding to respective signal values as a relation between the signal value and the luminous intensity of the fluorescent substance. However, measuring the luminous intensities of the fluorescent substances with respect to all the signal values leads to a tremendous number of measuring points. Thus this method is not a practical method. Thus, in many cases, by modeling the characteristics of the CRT and then obtaining parameters of that model formula from a small number of measuring points, the luminous intensities of fluorescent substances corresponding to signal values other than the measuring points are obtained from values calculated based on that model formula.
When the method using the model formula is applied to conversion from the luminous intensity to the signal value, the chromaticities of the respective fluorescent substances of RGB are measured by means of a colorimeter by preliminarily making the respective fluorescent substances of RGB to light to their maximum extent. The model formula for use in conversion processing from the luminous intensity to the signal value can be generally expressed for each of single colors in the following expression (1). EQU Y=Y.sub.0 +(Y.sub.c -Y.sub.0).multidot.(D/255).sup..gamma. (1)
where:
Y: luminance PA0 Y.sub.0 : luminance produced when the signal value is 0 PA0 Y.sub.c : luminance produced when the signal value is maximum PA0 D: arbitrary signal value PA0 Y: gamma characteristic value of CRT PA0 (Xa,Ya,Za) EQU .noteq.(X.sub.1, Y.sub.1, Z.sub.1)+(X.sub.2, Y.sub.2, Z.sub.2)+(X.sub.3, Y.sub.3, Z.sub.3) PA0 (Xa,Ya,Za): tristimulus values when (Ra, Ga, Ba)=(127, 127, 127) PA0 (X.sub.1, Y.sub.1, Z.sub.1): tristimulus values when (Ra,G.sub.0, B.sub.0)=(127, 0, 0) PA0 (X.sub.2, Y.sub.2, Z.sub.2): tristimulus values when (R.sub.0, Ga, B.sub.0)=(0, 127, 0) PA0 (X.sub.3, Y.sub.3, Z.sub.3): tristimulus values when (R.sub.0, G.sub.0, Ba)=(0, 0, 127)
The gamma characteristic value .gamma. in the above expression (1) is obtained from values obtained by preliminarily measuring the luminous intensity of each of RGB colors produced when a plurality of the signal values are given. In this manner, it is possible to obtain the luminous intensity of the fluorescent substance corresponding to the signal value at any points other than the measuring points by using the model formula in which the characteristic of the CRT is modeled.
On the other hand, if a relation between the luminous intensity and the signal value is expressed by LUT, the luminous intensities of each single color are measured for a plurality of the signal values and then those measured values are linear interpolated to obtain the luminous intensity corresponding to arbitrary signal value. Like this, instead of using the model formula, the luminous intensity of the fluorescent substance at points other than the measuring points corresponding to the signal value can be obtained by linear interpolation of the measured data. In this case, it is not necessary to consider an accuracy or the like of the model formula and even in actual CRT systems which do not always indicate an ideal behavior, a relation between the signal value and the luminous intensity of the fluorescent substance can be expressed.
However, there are some CRT systems which do not indicate an ideal behavior to additive mixture. For example, comparing a case in which each of the RGB colors is expressed in single color with a predetermined signal value with a case in which respective colors of the RGB colors are displayed at the same time by mixing with a predetermined signal value, the luminous intensity of each color is sometimes different despite the same signal value. In this case, it is difficult to reproduce a color at high precision according to the luminous intensity/signal value characteristic obtained by measuring a color expressed in single color. That is, tristimulus values obtained by synthesizing (adding) respective tristimulus values obtained when respective colors of RGB colors are displayed in single color do not coincide with tristimulus values obtained when respective RGB colors are displayed at same time, so that tristimulus values obtained when respective colors of RGB colors are displayed in single color does not match with tristimulus values obtained when respective RGB colors are displayed at same time (mismatching of additive mixture). For example, when the signal value is assumed to be 127, as shown in the following inequality, tristimulus values obtained by synthesizing tristimulus values measured when the respective colors of RGB are displayed in single color sometimes do not coincide with the tristimulus values measured when respective colors of RGB are displayed by mixing with the same signal value.
where
Because it is difficult to obtain data corresponding to the luminous intensity when producing hard copies of arbitrary chromaticity with a hard copy machine in which subtractive mixture is used, as shown in FIG. 2, arbitrary chromaticity 10 is converted to the signal value 22 such as cyan, magenta, yellow and black (thereafter referred to as CMYK) by conversion process 20 such as color estimation formula using the least square method in which a relation between the signal value and the chromaticity is expressed and three dimensional LUT (thereafter referred to as 3D-LUT). Meanwhile, because the subtractive mixture is capable of producing a color corresponding to K color by combination of respective colors of CMY, it is possible to construct the signal values with only CMY excluding K color.
As described above, to achieve high precision color reproduction with a color reproduction apparatus based on subtractive mixture, it is important to grasp a relation between the signal values of CMYK and the chromaticity. As a method for this purpose, there are analytic method using Neugebauer equation which is applicable only when reproducing colors in printing with halftone process, a statistical method such as the method of least squares and a method based on LUT. Further, considering that the characteristics of color reproduction of single color is different from the characteristics of color reproduction of mixing colors in subtractive mixture, a method of color reproduction by separating the process for single color from the process for mixing colors is known (see Japanese Patent Application Publication (JP-B) No. 7-123284). However, although the process for each single color is separated from the process for mixing colors in this technology, a relation between single color and mixing of colors are not considered sufficiently, so that it is difficult to obtain a sufficient precision of color reproduction. Further, because it is difficult to unify the single color characteristic of color material by a process for each single color, it is difficult to compensate for a difference in color for example between color material production lots.
As a method based on LUT, a method of color reproduction by utilizing single color LUT for analytical optical density is known (see Japanese Patent Application Publication (JP-B) No. 7-28426). Because colors are reproduced from only single color LUT at the time of output when this method is used, sufficient precision of color reproduction cannot be obtained. Further, because the single color LUT is adapted for analytical optical density, a number of processes are necessary for data unit management, measuring process and the like.
A method of color reproduction by utilizing 3D-LUT is known (see Japanese Patent Application Laid-Open (JP-A) Nos. 53-123201 and 56-14237). Although this method reproduces colors by using 3D-LUT, because characteristics different among the single colors are not taken into account, it is difficult to compensate for a difference in color between color material production lots. Thus, to improve precision of color reproduction by using 3D-LUT, a method using spline interpolation is known (see Japanese Patent Application Laid-Open (JP-A) No. 7-50760). According to this technology, the number of data must be cube of integer. For example, the number of data next to 125 (cube of 5) in data number is 216 (cube of 6) so that a tremendous number of data is necessary.
As described above, to improve precision of color reproduction in the hard copy apparatus, it is necessary to consider detailed tone reproduction characteristics of each color (heat generating temperatures/color material transfer amount characteristics). If this improvement is made in 3D-LUT, a great amount of storage capacity is required, high processing speed is required and production cost of the apparatus increases. Further, to obtain a relation between the signal value and the chromaticity directly and in detail, a great number of data is necessary. Further, when making various compensations for color reproduction, for example, compensating for a difference in color between the color material production lots, the 3D-LUT is required to be produced by performing measurement and arithmetic operation again so that the number of processes increases and the processing time increases. Further, when performing adjustment of tone (color adjustment), such as white balance adjustment, a treatment for distorting a partial or entire correspondence of the 3D-LUT is necessary so that process is very complicated.
As described above, according to the conventional color reproduction methods, the precision of color reproduction depends on a number of measuring points. To improve the precision, the number of the measuring points must be increased and a large number of measuring processes are needed. Because the characteristics of the CRT and hard copy machine change with a passage of time, it is necessary to measure the characteristics frequently and reflect the characteristics of the apparatus at that time for color reproduction. However, a great number of preparatory steps for measurement or the like become an obstacle to maintaining high precision of color reproduction. Further, in an office or the like in which many CRTs and hard copy machines are used, if the number of preparatory steps for respective apparatuses increases, it becomes difficult to maintain color reproduction precision in all the apparatuses.
Further, when reproducing colors with a hard copy machine, it is difficult, different from a case in which color reproduction is made on the CRT, to express the characteristics of ink which originates color production by model formula, different from a case in which color reproduction is made on the CRT, and the characteristic of non-linearity is strong. Thus, to obtain sufficient precision by using a method based on linear interpolation, a great number of measurements are needed.